ORIGINAL ARTICLE

Multiple process parameter optimization of wire electricaldischarge machining on Inconel 825 using Taguchi greyrelational analysis

G. Rajyalakshmi & P. Venkata Ramaiah

Received: 30 August 2011 /Accepted: 20 May 2013# Springer-Verlag London 2013

Abstract In this paper, an effective approach, Taguchi greyrelational analysis, has been applied to experimental resultsof wire cut electrical discharge machining (WEDM) onInconel 825 with consideration of multiple response mea-sures. The approach combines the orthogonal array designof experiment with grey relational analysis. The main ob-jective of this study is to obtain improved material removalrate, surface roughness, and spark gap. Grey relational the-ory is adopted to determine the best process parameters thatoptimize the response measures. The experiment has beendone by using Taguchi’s orthogonal array L36 (21×37).Each experiment was conducted under different conditionsof input parameters. The response table and the grey rela-tional grade for each level of the machining parameters havebeen established. From 36 experiments, the best combina-tion of parameters was found. The experimental resultsconfirm that the proposed method in this study effectivelyimproves the machining performance of WEDM process.

Keywords Inconel 825 .Wire cut EDM . Taguchi greyrelational analysis . Optimization

1 Introduction

1.1 Wire EDM

Wire electrical discharge machining (WEDM) is one of theimportant nontraditional machining processes which areused for machining difficult to machine materials like com-posites and intermetallic materials. Intricate profiles used inprosthetics and biomedical applications can also be done inWEDM. WEDM involves complex physical and chemicalprocess including heating and cooling. The electrical dis-charge energy affected by the spark plasma intensity and thedischarging time will determine the crater size, which in turnwill influence the machining efficiency and surface quality.

InWEDM, also known as wire cut EDM andwire cutting, athin single-strand metal wire, usually brass, is fed through theworkpiece and submerged in a tank of dielectric fluid, typicallydeionized water. Wire cut EDM is typically used to cut platesas thick as 300 mm and to make punches, tools, and dies fromhard metals that are difficult to machine with other methods.

The wire, which is constantly fed from a spool, is heldbetween upper and lower diamond guides. The guides, usuallyCNC controlled, move in the x–y plane. Onmost machines, theupper guide can also move independently in the z–u–v axis,giving rise to the ability to cut tapered and transitioning shapes(circle on the bottom square at the top for example). The upperguide can control axis movements in x–y–u–v–i–k–l. Thisallows the wire cut EDM to be programmed to cut veryintricate and delicate shapes.

The upper and lower diamond guides are usually accurate to0.004 mm and can have a cutting path or kerf as small as0.12 mm using a Ø 0.1 mm wire, though the average cutting

G. Rajyalakshmi (*)School of Mechanical and Building Sciences, VIT University,Vellore, Tamilnadu 632014, Indiae-mail: rajyalakshmi@vit.ac.in

P. Venkata RamaiahDepartment of Mechanical Engineering, Sri VenkateswaraUniversity, Tirupati, Andhra Pradesh 517 502, Indiae-mail: pvenkataramaiah@gamil.com

Int J Adv Manuf TechnolDOI 10.1007/s00170-013-5081-z

kerf that achieves the best economic cost and machining timeis 0.335 mm using Ø 0.25 brass wire. The reason that thecutting width is greater than the width of the wire is becausesparking occurs from the sides of the wire to the workpiece,causing erosion. This “overcut” is necessary; for many appli-cations, it is adequately predictable and therefore can be com-pensated for (for instance in micro-EDM, this is not often thecase). Spools of wire are long—an 8-kg spool of 0.25mmwireis just over 19 km in length. Wire diameter can be as small as20 μm and the geometry precision is not far from ±1 μm.

The wire cut process uses water as its dielectric fluid,controlling its resistivity and other electrical properties withfilters and deionizer units. The water flushes the cut debrisaway from the cutting zone. Flushing is an important factorin determining the maximum feed rate for a given materialthickness (Fig. 1).

Along with tighter tolerances, multi-axis EDM wire cut-ting machining center has added features such as multi-heads for cutting two parts at the same time, controls forpreventing wire breakage, automatic self-threading featuresin case of wire breakage, and programmable machiningstrategies to optimize the operation.

Wire cutting EDM is commonly used when low residualstresses are desired because it does not require high cuttingforces for removal of material. If the energy/power per pulseis relatively low (as in finishing operations), little change inthe mechanical properties of a material is expected due tothese low residual stresses, although material that has notbeen stress relieved can distort in the machining process.

The workpiece may undergo a significant thermal cycle;its severity depending on the technological parameters used.Such thermal cycles may cause formation of a recast layeron the part and residual tensile stresses on the workpiece.

With the introduction and increased use of newer andharder materials like titanium, hardened steel, high-strengthtemperature-resistant alloys, fiber-reinforced composites,and ceramics in aerospace, nuclear, missile, turbine, auto-mobile, and tool and die making industries, a different class

of machining process has emerged. Better finish, low toler-ance, higher production rate, miniaturization, etc. are alsothe present demands of the manufacturing industries.

In recent years, wire EDM has become an importantnontraditional machining process, which is widely used inthe aerospace and automotive industries. However, selectionof cutting parameters for obtaining higher cutting efficiency oraccuracy in wire EDM is still not fully solved, even with themost up-to-date CNC wire EDM machine. This is mainly dueto the complicated stochastic process mechanisms in wireEDM. As a result, the relationships between the cutting pa-rameters and cutting performance are hard to model accurately.

1.2 Literature survey

In EDM, it is important to select machining parameters forachieving optimal machining performance [1]. Usually, thedesired machining parameters are determined based on ex-perience or on handbook values. However, this does notensure that the selected machining parameters result inoptimal or near optimal machining performance for thatparticular electrical discharge machine and environment.

Mahapatra et al. [2] explained the method of optimizationof WEDM process parameters using Taguchi method. It hasbeen shown that the grey-based Taguchi method can opti-mize the multi-response processes through the settings ofthe process parameters [3] but, in this paper, the grey rela-tional analysis is not used for calculating the S/N ratio. Thisis because grey relational analysis based on the grey systemtheory [4] is used for solving the complicated interrelation-ships among the multiple responses. A grey relational gradeis then obtained for analyzing the relational degree of themultiple responses. The fuzzy-based Taguchi method canalso be used to optimize the multi-response process throughthe settings of process parameters [5].

Chung-Feng et al. [6] examined multiple quality optimi-zation of the injection molding for polyether ether ketone.This study looked into the dimensional deviation andstrength of screws produced by the injection molding. Thisstudy applied the Taguchi method to cut down on thenumber of experiments and combined grey relational anal-ysis to determine the optimal processing parameters formultiple quality characteristics. Tosun [7] used the greyrelational analysis for the determination of optimal drillingparameters with the objective of minimization of surfaceroughness and burr height. Lin et al. [8] used the greyrelational analysis method for optimization of the EDMprocess. Most of the applications of Taguchi method con-centrate on the optimization of single response problems [4].The grey relational analysis based on grey system theorycan be used for solving the complicated interrelationshipsamong the multi-responses [4, 9, 10]. A grey relationalgrade is obtained to evaluate the multiple responses. As aFig. 1 Wire cut EDM process [2]

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result, optimization of the multiple responses can beconverted into optimization of a single relational grade. Inshort, there is an ample scope of applying the proposedmethodology of grey relational analysis and Taguchi meth-od with the multiple responses for the optimization.

It may be noted that most of the prevailing approaches haveused complex mathematical or statistical methods such asANN, dual response approach, genetic algorithm, simulatedannealing, and linear or nonlinear or dynamic programming.These approaches are difficult to implement by individualswith little background in mathematics/statistics and so are oflittle practical use. Ramakrishnan et al. [11] also lack the wayto convert multiple objectives into a single objective formatthough the method is relatively simple. Through the greyrelational analysis (GRA), a grey relational grade is obtainedto evaluate the multiple performance characteristics. For ex-ample, Hsiao et al. [12] used the TM with GRA to optimizethe plasma arc welding process. Prabhu et al. [13] analyzedsurface characteristics like surface roughness andmicro cracksof Inconel 825 and found out that an excellent machined nanofinish can be obtained by setting the machining parameters atoptimum level. The Taguchi design of experimental techniqueis used to optimize the machining parameters and an L9orthogonal array is selected [13]. Grey relational analysiscan be recommended as a method for optimizing the compli-cated interrelationships among multiple performance charac-teristics [14–17]. Moreover, Lin et al. showed that grey rela-tional analysis is more straightforward than the fuzzy-basedTaguchi method for optimizing the EDM process withmultiple process responses [18]. Khan [19] presented hisanalysis on material removal rate during EDM of alu-minum and mild steel using copper and brass electrodes.The highest material removal rate was observed duringmachining of aluminum due to high thermal conductiv-ity and low melting point when compared to steel atlow thermal conductivity and high melting point. As aresult, highest material removal rates were obtainedduring machining of aluminum alloy.

Inconel 825 is a nickel-based high-temperature strengthalloy which is useful for applications in aerospace, missile,nuclear power, chemical and petrochemical, heat treatment,marine, and space shuttle components. The characteristicssuch as higher strain hardening tendency, high dynamicshear strength, and poor thermal diffusivity are the majorcauses of difficulty in machining of this alloy. These, inturn, produce higher cutting forces, highly strain hardenedand toughened chips, and excessive tool wear and causesurface damages extending to subsurface levels. Besides,various processes, cutting tool, and work material-relatedparameters have complex interactions during machining. Allthese effects, in general, hamper the machinability of thisalloy. There is a complex interrelation between processingconditions and output variables in Fig. 2.

Thus, selecting the best machining conditions duringmachining, which introduces high material removal rateand surface quality, is really a tough task. It is found,though, from the machining literature that a very few au-thors conducted parameter optimization in machining ofInconel 825. No study has been available on Inconel 825machining with multi-objective optimization.

This paper presents the optimization of wire electricaldischarge machining of Inconel 825 process so as to opti-mize the responses using Taguchi-based grey relationalanalysis (TGRA). Eighteen experimental runs based onTaguchi orthogonal array were conducted to determine thebest factor level combination. The factor levels wereassessed according to the three response variables, namelymaterial removal rate (MRR), surface roughness (SR), andspark gap (SG). The influence of the control factors on theseresponse variables was studied by assessing the single greyrelational grade for all performance characteristics. Huang etal. [20] investigated experimentally the effect of machiningparameters on the gap width, the surface roughness, and thedepth of white layer on the machined workpiece surface.

The outline of the paper is as follows. The paper beginswith the experimental plan and procedure followed by theTaguchi analysis of the observed data. Then, TGRA of themultiple responses is discussed in detail. Analysis of vari-ance (ANOVA) of the grey relational grade has beenperformed to predict the optimum parameters. In the lastsection of the paper, experimental validation of the results iscarried out.

2 Materials and methods

2.1 Work material

Due to their high-temperature mechanical strength and high-corrosion resistance properties, super alloys are nowadaysused in marine, space, and other applications. Their abilityto maintain their mechanical properties at high temperaturesseverely hinders the machinability of these alloys [21, 22].Its poor thermal diffusivity generates high temperature at thetool tip as well as high thermal gradients in the cutting tool,affecting the tool life adversely. Inconel 825 is very chem-ically reactive and therefore has a tendency to weld to thecutting tool during machining, thus leading to prematuretool failure. Owing to all these problems, it is very difficultto machine Inconel 825 by conventional machining process-es and moreover by conventionally used tool materials.

Of late, modern machining techniques such as WEDMare increasingly being used for machining such hard mate-rials. Hence, this study focused on machining of Inconel 825using WEDM in order to satisfy production and qualityrequirement.

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The compositional range for Inconel 825 is provided inTable 1 and typical properties are covered in Table 2.

2.2 Experimental setup and experimental procedure

2.2.1 Schematic of machining

The experiments were carried out on Ultra Cut 843/ULTRACUT f2 CNC WEDM machine. In this machine, all the axesare servo controlled and can be programmed to follow aCNC code which is fed through the control panel. All threeaxes have an accuracy of 1 μm. The electrode material usedwas a 0.25-mm diameter brass wire. A small gap of 0.025 to0.05 mm is maintained in between the wire and workpiece.The high-energy density erodes material from both the wireand workpiece by local melting and vaporizing. The dielec-tric fluid (deionized water) is continuously flushed throughthe gap along the wire and to the sparking area to removethe debris produced during the erosion. A collection tank islocated at the bottom to collect the used wire erosions andthen discarded. The wires once used cannot be reused again,due to the variation in dimensional accuracy. Through anNC code, machining can be programmed. Wire cut electricaldischarge machining of Inconel 825 alloy has been consid-ered in the present set of research work.

The size of the workpiece considered for experimentationon the wire cut EDM is 10 mm width, 10 mm length, and15 mm depth of cut. According to the Taguchi method basedon robust design, a L36 (21×37) mixed orthogonal array isemployed for the experimentation. Each experiment wasrepeated two times and an average of two readings is takenfor analysis. Totally, 72 workpieces are cut for this analysis.

In setting the machining parameters, particularly in roughcutting operation, the goal is threefold—the maximizationof MRR, minimization of SR, and minimization of gapwidth. Generally, the machine tool builder provides machin-ing parameter table to be used for setting machining param-eter. This process relies heavily on the experience of theoperators. In practice, it is very difficult to utilize the opti-mal functions of a machine owing to there being too manyadjustable machining parameters. With a view to alleviatethis difficulty, a simple but reliable method based on statis-tically designed experiments is suggested for investigatingthe effects of various process parameters on MRR, SR, andgap width and determines optimal process settings. In thepresent work, data have been collected from few experimen-tal runs with randomly chosen factor combinations. A qua-dratic model has been fitted for identification of the processto establish approximate interrelation among various pro-cess parameters as well as response variables. These math-ematical models have been utilized to generate data as perTaguchi design. Finally, grey-based Taguchi technique hasbeen adopted to evaluate the optimal process environment.

Among the eight WEDM parameters, two levels for onecontrol factor (pulse on time) and three levels for remainingseven control factors are considered for optimality analysisduring machining of Inconel 825 alloy. Figure 3 shows theworkpiece after WED machining.

2.3 Machining parameter selection and performanceevaluation

The selection of optimum machining parameters in WEDMis an important step. Improperly selected parameters mayresult in serious problems like short circuiting of wire, wirebreakage, and work surface damage which is imposingcertain limits on the production schedule and also reducingproductivity. As MRR, SR, and SG are most importantresponses in WEDM; various investigations have been car-ried out by several researchers for improving the MRR,surface finish, and kerf width [3–7]. However, the problemof selection of machining parameters is not fully dependingon machine controls rather on material dependence.

To perform the experimental design, the levels of ma-chining parameters are selected as in Table 3.

Inconel825Wire EDM machining

MATERIAL REMOVAL

RATE

SURFACE ROUGHNESS

SPARK GAP

PULSE ON TIME

PULSE OFF TIME

CORNER SERVO VOLTAGE

FLUSHING PRESSURE

WIRE FEED

WIRE TENSION

SPARK GAP VOLTAGE

SERVO FEED RATE

Fig. 2 Interaction betweenprocessing conditions andoutput variables

Table 1 Chemicalcomposition of Inconel825

Element Content (%)

Ni 38–46

Fe 22

Cr 19.5–23.5

Mo 2.5–3.5

Cu 1.5–3

Ti 0.6–1.2

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3 Experimental results and discussions

The multiple responses from the experiment were calculatedas follows:

Material removal rate is calculated as:

MRR ¼ V c � b � h mm3= min

Where:

V Cutting speed in millimeters per minuteb Width of cut in millimeterh Height of the workpiece in millimeter and surface

roughness is measured with SurfcorderSE3500 inmicrometer and spark gap is measured with micrometerin millimeter

Statistical analysis was carried out on the experimentaldata obtained through Taguchi experimental design usingstatistical software Minitab 14. ANOVA was performed todetermine the influence of input parameters on the outputresponse variables. Since the major focus of this study is ongrey relational analysis, the results of Taguchi experimentshave not been elaborated here. This section therefore hastwo subsections. The first subsection discusses the results ofTaguchi method experiments briefly. The second subsectionon the results discusses the application of grey relationalanalysis in detail (Table 4).

3.1 Statistical results based on Taguchi analysis

Statistical analysis of the individual performance char-acteristics was carried out to determine the influence ofthe control factors on the response variables. Table 5shows the ANOVA results for the chosen performancecharacteristics—spark gap, material removal rate, and surfaceroughness.

3.2 Optimization steps using Taguchi grey method

In our case, the problem has eight performance characteristicsthat need to be minimized by choosing appropriate processingconditions. They are material removal rate, spark gap, andsurface roughness. In such cases, the problem is convertedinto a single objective problem using grey relational analysis(see Fig. 4). The grey relational analysis deals with the ranksand not with the real value of the grey relational grade [23].

3.2.1 Approach of the present investigation

The wire electrical discharge machining process to be in-vestigated corresponds to 36 different experiments. For theGRA, these 36 experiments become 36 subsystems. Theinfluence of these subsystems on the response variable isto be analyzed using the GRA technique [24]. Hence, theprocess (system) is assessed by conducting 36 experiments(subsystems) where each experiment is termed as compara-bility sequences were obtained. The parametric conditionscorresponding to the highest grey relational grade giveminimum values of the spark gap and the surface roughnessand maximum value of the material removal rate. In thismanner, the multi-objective problem has been convertedinto single objective optimization using the GRA technique.

3.2.2 Formulation of the problem

Thus, the multi-objective optimization problem under inves-tigation can be stated as “minimize: f (SG, SR)” and max-imize: f (MRR), subject to independent decision variablesas: pulse on time T ON (in microsecond), pulse off time TOFF (in microsecond), corner servo voltage (volts), flushingpressure WP (in kilograms per centimeter), wire feed rateWF (in meters per minute), wire tensionWT (in kilogram-force),

Table 2 Properties of Inconel825 Property Metric Imperial

Density 8.14 g/cm3 0.294 lb/in.3

Melting point 1,400 °C 2,550 °F

Coefficient of expansion 14.0 m/m/°C (20–100 °C) 7.8×10−6 in./in./°F (70–212 °F)

Modulus of rigidity 75.9 N/mm2 11,009 ksi

Modulus of elasticity 196 kN/mm2 28,428 ksi

Fig. 3 Workpiece after wire cut electrical discharge machining

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spark gap voltage SV (volts), and servo feed rate SF (in milli-meters per minute). The range of the independent decision vari-ables should be: 105≤TON≤115; TOFF, 50≤55≤60; CS, 50≤60≤70; WP, 8≤10≤15; WF, 2≤5≤6; WT, 9≤10≤11; SV, 20≤25≤30; and SF, 1,050≤1,100≤1,150. Furthermore, the abovemulti-objective problem can be converted into a single optimi-zation problem using grey relational grade as “maximize greyrelational grade (GRG); 0≤GRG≤1,” subjected to independentdecision variables in the range mentioned above.

3.2.3 Methodology

The stepwise procedure of GRA optimization shown in theflowchart (see Fig. 5) is used to solve the above formulation.The absolute value of data difference between comparabilitysequences could be used to measure approximate correlationbetween these sequences in terms of grey relational grade.

Step 1 Normalization of S/N ratioIt is the first step in the grey relational analysis; a

normalization of the S/N ratio is performed to prepareraw data for the analysis where the original sequence istransferred to a comparable sequence. Linear normali-zation is usually required since the range and unit in onedata sequence may differ from the others. A linearnormalization of the S/N ratio in the range between zeroand unity is also called as the grey relational generation[5]. Further analysis is carried out based on these S/Nratio values. The material removal rate is a higher-the-better performance characteristic, since the maximiza-tion of the quality characteristic of interest is sought andcan be expressed as:

S=N ratio ¼ −log10 1=n� � Xn

i ¼ 1

1

y2ijð1Þ

Where

n Number of replications andyij Observed response value

Where i=1, 2 …n; j=1, 2 …k.The surface roughness and spark gap are the

lower-the-better performance characteristic andthe loss function for the same can be expressed as:

S=N ratio ¼ −log10 1=n� � Xn

i ¼ 1

y2ij ð2Þ

Step 2 Determination of deviation sequences, Δ0i(k)The deviation sequence Δ0i(k) is the absolute the

reference sequence x 0*(k) and the comparability

sequence x i*(k) after normalization. It is deter-

mined using Eq. 3:

Δ0i kð Þ ¼ x�0 kð Þ−x�i kð Þ�� ��: ð3Þ

Step 3 Calculation of grey relational coefficient (GRC)GRC for all the sequences expresses the re-

lationship between the ideal (best) and actualnormalized S/N ratio. If the two sequencesagree at all points, then their grey relationalcoefficient is 1; + (x0(k), xi(k)) can be expressedby Eq. 4 [15].

g x0 kð Þ; xi kð Þð Þ ¼ Δminþ ξΔmax

Δ0i kð Þ þ ξΔmaxð4Þ

where Δmin is the smallest value of Δ0i(k)=min imink|x 0

*(k)−x 0*(k)| and Δmax is the larg-

est value of Δ0i kð Þ ¼ maximaxk x�0 kð Þ−x�ikð Þ�� ��,

x 0*(k) is the ideal normalized S/N ratio, x i

*(k)is the normalized comparability sequence, and ζis the distinguishing coefficient. The value of ζcan be adjusted with the systematic actual needand defined in the range between 0 and 1,ζ∈[0, 1]. It will be 0.5 generally [15].

Step 4 Determination of GRGThe overall evaluation of the multiple perfor-

mance characteristics is based on the grey rela-tional grade. The grey relational grade [5] is an

Table 3 Experimental factors and their levels for wire electrical discharge machining process

Sample no. Factor Parameter Symbol Level 1 Level 2 Level 3 Range of process parameters

1 A Pulse on time T on (μs) 105 115 – 105–115

2 B Pulse off time T off (μs) 50 55 60 50–60

3 C Corner servo CS (volts) 50 60 70 50–70

4 D Flushing pressure of dielectric fluid WP (kg/cm2) 8 10 15 8–15

5 E Wire feed rate WF (m/min) 2 5 6 2–6

6 F Wire tension N WT (kg-f) 9 10 11 9–11

7 G Spark gap voltage SV (volts) 20 25 30 20–30

8 H Servo Feed SF (mm/min) 1,050 1,100 1,150 1,050–1,150

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average sum of the grey relational coefficientswhich is defined as follows:

g x0; xið Þ ¼ 1

m∑m

i ¼ 1g x0 kð Þ; xi kð Þð Þ ð5Þ

where + (x0, xi) is the grey relational grade forthe jth experiment and m is the number ofperformance characteristics

If the two sequences agree at all points, thentheir grey relational coefficient is 1 everywhere,

and therefore, their grey relational grade isequal to 1. In view of this, the relational gradeof two comparing sequences can be quantifiedby the mean value of their grey relational co-efficients and the grey relational grade. Thegrey relational grade also indicates the degreeof influence that a comparability sequence couldexert over the reference sequence. Therefore, ifa particular comparability sequence is more impor-tant than the other comparability sequences to thereference sequence, then the grey relational grade for

Table 4 Experimental layout using an L36 orthogonal array and experimental results

Experiment no. T on T off CS WP WF WT SV SF MRR (mm3/min) SR (μm) SG (mm)

1 1 1 1 1 1 1 1 1 120.375 1.54 0.0250

2 1 2 2 2 2 2 2 2 143.250 1.86 0.0350

3 1 3 3 3 3 3 3 3 182.250 1.41 0.0375

4 1 1 1 1 1 2 2 2 119.625 1.68 0.0150

5 1 2 2 2 2 3 3 3 139.500 1.66 0.0450

6 1 3 3 3 3 1 1 1 183.750 1.75 0.0150

7 1 1 1 2 3 1 2 3 112.875 1.47 0.0450

8 1 2 2 3 1 2 3 1 142.500 1.17 0.0500

9 1 3 3 1 2 3 1 2 195.750 1.99 0.0450

10 1 1 1 3 2 1 3 2 114.750 1.86 0.0400

11 1 2 2 1 3 2 1 3 147.750 1.54 0.0450

12 1 3 3 2 1 3 2 1 202.125 1.94 0.0450

13 1 1 2 3 1 3 2 1 115.875 1.86 0.0350

14 1 2 3 1 2 1 3 2 127.125 1.85 0.0150

15 1 3 1 2 3 2 1 3 144.375 1.61 0.0400

16 1 1 2 3 2 1 1 3 123.375 1.94 0.0450

17 1 2 3 1 3 2 2 1 131.625 1.38 0.0400

18 1 3 1 2 1 3 3 2 187.125 1.47 0.0400

19 2 1 2 1 3 3 3 1 371.250 1.91 0.0500

20 2 2 3 2 1 1 1 2 315.375 1.88 0.0100

21 2 3 1 3 2 2 2 3 325.500 2.58 0.0400

22 2 1 2 2 3 3 1 2 277.875 2.03 0.0400

23 2 2 3 3 1 1 2 3 294.375 2.30 0.0150

24 2 3 1 1 2 2 3 1 309.375 1.91 0.0350

25 2 1 3 2 1 2 3 3 267.375 1.94 0.0100

26 2 2 1 3 2 3 1 1 329.250 1.95 0.0300

27 2 3 2 1 3 1 2 2 325.875 2.25 0.0350

28 2 1 3 2 2 2 1 1 264.750 2.23 0.0500

29 2 2 1 3 3 3 2 2 247.875 2.04 0.0400

30 2 3 2 1 1 1 3 3 352.250 2.44 0.0150

31 2 1 3 3 3 2 3 2 401.250 2.05 0.0100

32 2 2 1 1 1 3 1 3 348.750 2.94 0.0300

33 2 3 2 2 2 1 2 1 360.000 2.32 0.0350

34 2 1 3 1 2 3 2 3 322.500 1.90 0.0450

35 2 2 1 2 3 1 3 1 352.500 1.82 0.0350

36 2 3 2 3 1 2 1 2 274.875 2.30 0.0450

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that comparability sequence and reference sequencewill be higher than other grey relational grades [15].

Step 5 Determination of optimum parametersThe grey relational grade calculated for each

sequence is taken as a response for the furtheranalysis. The larger-the-better quality characteristicwas used for analyzing the GRG, since a largervalue indicates the better performance of the

process. The quality characteristics used is givenby Eq. 1 [4]. The number of repeated test is one,since only one relational grade was acquired ineach group for this particular calculation of S/N.The grey relational grade obtained using Eq. 5 isanalyzed using analysis of variance (ANOVA).ANOVA is used to reveal the level of significanceof influence of factor(s) on a particular response.

Table 5 Analysis of variance(ANOVA) for response variables ANOVA for MRR

Source df Sum of squares Mean sum of squares F ratio % contributionA 1 268,151 268,151 200.202 81.618

B 2 8,398 4,199 3.1341 2.68

C 2 1,326 663 0.4949 0.423

D 2 853 427 0.31879 0.272

E 2 968 484 0.36315 0.309

F 2 2,570 1,285 .9593 0.821

G 2 3,051 1,526 1.139 0.974

H 2 1,089 545 .4069 0.347

Error 20 26,788 1,339.42

Total 35 313,194

ANOVA for SG

Source df Sum of squares Mean sum of squares F ratio % contribution

A 1 0.000213 0.000213 1.695 3.76

B 2 0.000059 0.000029 0.232 1.043

C 2 0.000792 0.000396 3.168 14.012

D 2 0.000057 0.000028 0.224 1.008

E 2 0.000719 0.000360 2.88 12.72

F 2 0.000973 0.000487 3.896 17.21

G 2 0.000090 0.000045 0.36 1.592

H 2 0.000236 0.000118 0.944 4.175

Error 20 0.002513 0.000125

Total 35 0.005652

ANOVA for SR

Source df Sum of squares Mean sum of squares F ratio % contribution

A 1 2.1560 2.1560 32.93 47.56

B 2 0.137 0.068 1.038 3.02

C 2 0.019 0.009 0.4526 0.419

D 2 0.061 0.030 0.4583 1.345

E 2 0.360 0.180 2.749 7.942

F 2 0.061 0.030 0.4583 1.345

G 2 0.257 0.129 1.97 5.669

H 2 0.173 0.086 1.313 3.82

Error 20 1.3093 0.065465

Total 35 4.5333

Multi objective

optimization

GreyRelationalAnalysis

Single objective

optimization

Fig. 4 Purpose of greyrelational analysis

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This is accomplished by separating the total vari-ability of the grey relational grades, which is mea-sured by the sum of the squared deviations from thetotal mean of the grey relational grade, into contri-butions by each process parameter and the error.The response table of Taguchi method wasemployed here to calculate the average grey rela-tional grade for each factor level. In this, the group-ing of the grey relational grades was done initiallyby the factor level for each column in the orthogo-nal array and then by averaging them.

4 Application of grey relational analysis

We know from the analysis of machining process that the higherthe material removal rate and lower spark gap as well as lowervalue of surface roughness provide better quality of themachinedsurface. Thus, the data sequences of material removal rate, sparkgap, and surface roughness have “larger-the-better” and “smaller-the-better” characteristics, respectively. The smaller-the-bettermethodology as expressed in Eqs. 1 and 2 was used for deter-mining the S/N ratio. The S/N ratio values of the response vari-ables are shown in Table 6. The S/N ratio values were normalizedusing Eq. 3. All the sequences after normalization are denoted asx0

*(k) and xi*(k) for reference sequence and comparability se-

quence, respectively. The larger value of normalized results canindicate the better performance characteristic, and the best-normalized results will be equal to 1. Then, the deviation se-quencesΔ0i(k)=|x0

*(k)−xi*(k)| are determined using Eq. 3. Next,

the grey relational coefficient is calculated. In this study, all themachining parameters influence the material removal rate, sparkgap, and surface roughness, moreover, equally. Considering thatall the process parameters are of equal weighting, thedistinguishing coefficient ζ=0.5 was substituted in Eq. 4. Then,the grey relational grade was determined by Eq. 5. Table 7 showsthe grey relational grade for each experiment using the L36orthogonal array. A higher grey relational grade indicates thatthe corresponding S/N ratio is closer to the ideally normalizedS/N ratio. It is observed that experiment 3 has the highest greyrelational grade (see Table 7); it therefore can be considered as abest experimental sequence for multiple performance of theprocess. Furthermore, the order of the experiments according tothe values of grey relational grade is depicted in Table 7. Taguchimethod is used to analyze the grey relational grades obtained.The calculated grey relational grade was taken as the responsevalue in the Taguchi method. The mean response table for theoverall grey relational grade is shown in Table 8 and is repre-sented graphically in Fig. 8. The ordinate of Fig. 7 represents themeans of grey relational grade calculated using larger-the-bettercriteria using Eq. 1. The steep slope of grey relational gradegraph indicates more influence of machining parameters in theperformance characteristics. Basically, the larger the grey rela-tional grade, the better are the multiple performance characteris-tics. From the grey relational grade graph, the optimal parametriccombination was determined. The optimal factor setting is A1,B1, C1, D1, E1, F2, G2, and H2, Similar results were observedby the others during machining of this alloy at higher cuttingspeeds [25, 26]. At a higher cutting speed, the surface flaws anddiscontinuities get wiped out due to higher thermal influence in

ComparabilitySequences

Step5

R Responsevariables

Step4

Input parameters

Step 1 Step2 Step3

Wire electrical discharge machining

Grey system

Experimental runs 1-36

MRR, SG, SR

S/N ratio of 1-36experiments

S/N ratio

normalization,

1-18

Grey relational coefficient 1-36

Single grey relational grade

Single processing condition

TGRA

Fig. 5 Stepwise procedure of GRA optimization

Int J Adv Manuf Technol

the machining region. Therefore, significant reduction inthe surface roughness is observed [27, 28]. Furthermore,it facilitates the easy removal of the work material dueto reduced dynamic shear strength of Inconel 825 in thepresence of higher thermal influence in the machiningregion. Therefore, lower forces are produced duringmachining [27, 28]. Thus, the overall machining perfor-mance is higher and reflects in the higher value of thegrey-related grade. A similar increase in the surfaceroughness was mentioned by Pawade et al. [26]. Thistrend could be due to complex deformation pattern of

this material, which involves excessive strain hardening;therefore, the overall machining performance is better ata higher value of GRG (Figs. 6, 7, and 8).

5 ANOVA

The results obtained from the experiments were analyzedusing analysis of variance to find the significance of eachinput factor on the measures of process performances, ma-terial removal rate, surface roughness, and spark gap. Using

Table 6 The S/N ratio values for the experimental results

Experiment number A B C D E F G H S/N ratio, MRR S/N ratio, surface roughness S/N ratio, spark gap

1 1 1 1 1 1 1 1 1 41.6107 −3.75041 32.0412

2 1 2 2 2 2 2 2 2 43.1219 −5.39026 29.1186

3 1 3 3 3 3 3 3 3 45.2134 −2.98438 28.5194

4 1 1 1 1 1 2 2 2 41.5564 −4.50619 36.4782

5 1 2 2 2 2 3 3 3 42.8915 −4.40216 26.9357

6 1 3 3 3 3 1 1 1 45.2845 −4.86076 36.4782

7 1 1 1 2 3 1 2 3 41.052 −3.34635 26.9357

8 1 2 2 3 1 2 3 1 43.0763 −1.36372 26.0206

9 1 3 3 1 2 3 1 2 45.834 −5.97706 26.9357

10 1 1 1 3 2 1 3 2 41.1951 −5.39026 27.9588

11 1 2 2 1 3 2 1 3 43.3905 −3.75041 26.9357

12 1 3 3 2 1 3 2 1 46.1124 −5.75603 26.9357

13 1 1 2 3 1 3 2 1 41.2798 −5.39026 29.1186

14 1 2 3 1 2 1 3 2 42.0846 −5.34343 36.4782

15 1 3 1 2 3 2 1 3 43.1898 −4.13652 27.9588

16 1 1 2 3 2 1 1 3 41.8245 −5.75603 26.9357

17 1 2 3 1 3 2 2 1 42.3868 −2.79758 27.9588

18 1 3 1 2 1 3 3 2 45.4426 −3.34635 27.9588

19 2 1 2 1 3 3 3 1 51.3933 −5.62067 26.0206

20 2 2 3 2 1 1 1 2 49.9765 −5.48316 40

21 2 3 1 3 2 2 2 3 50.251 −8.23239 27.9588

22 2 1 2 2 3 3 1 2 48.877 −6.14992 27.9588

23 2 2 3 3 1 1 2 3 49.378 −7.23456 36.4782

24 2 3 1 1 2 2 3 1 49.8097 −5.62067 29.1186

25 2 1 3 2 1 2 3 3 48.5424 −5.75603 40

26 2 2 1 3 2 3 1 1 50.3505 −5.80069 30.4576

27 2 3 2 1 3 1 2 2 50.261 −7.04365 29.1186

28 2 1 3 2 2 2 1 1 48.4567 −6.9661 26.0206

29 2 2 1 3 3 3 2 2 47.8847 −6.1926 27.9588

30 2 3 2 1 1 1 3 3 50.937 −7.7478 36.4782

31 2 1 3 3 3 2 3 2 52.0683 −6.23508 40

32 2 2 1 1 1 3 1 3 50.8503 −9.36695 30.4576

33 2 3 2 2 2 1 2 1 51.1261 −7.30976 29.1186

34 2 1 3 1 2 3 2 3 50.1706 −5.57507 26.9357

35 2 2 1 2 3 1 3 1 50.9432 −5.20143 29.1186

36 2 3 2 3 1 2 1 2 48.7827 −7.23456 26.9357

Int J Adv Manuf Technol

the grey grade value, ANOVA is formulated for identifyingthe significant factors. The results of ANOVA are presentedin Tables 9 and 10.

The results of the ANOVA are represented in the table above,and from the table, it is clear that pulse on time is the majorinfluencing factor (contributing 50.18 % to performance mea-sures), followed by pulse off time (contributing 14.19 %), wiretension (contributing 11.79 %), wire feed (contributing 4.29 %),corner servo voltage (contributing 2.14 %), spark gap voltage(contributing 2.06 %), servo voltage (contributing 1.19 %), andflushing pressure (contributing 0.87 %).

Table 7 Grey relational coefficients and grey grade

Experiment number GRC material removal rate GRC surface roughness GRC spark gap Grey relational grade Rank

1 0.9079 0.6264 0.4675 0.6672 6

2 0.7269 0.4984 0.3911 0.5388 18

3 0.5696 0.71174 0.3784 0.5532 17

4 0.9162 0.562 0.6649 0.7144 1

5 0.7497 0.5684 0.3485 0.5555 16

6 0.5654 0.5336 0.6649 0.5879 13

7 1 0.6686 0.3485 0.6724 4

8 0.7313 1 0.3333 0.6882 3

9 0.5353 0.46449 0.3485 0.5097 20

10 0.9748 0.4985 0.3672 0.6135 11

11 0.7019 0.6264 0.3485 0.5589 14

12 0.5212 0.4767 0.3485 0.4488 23

13 0.9604 0.4984 0.3911 0.6166 10

14 0.8421 0.5014 0.6649 0.6695 5

15 0.7169 0.5906 0.3672 0.5582 15

16 0.877 0.8795 0.3485 0.7077 2

17 0.8049 0.7362 0.3672 0.6361 7

18 0.5564 0.6686 0.3672 0.5307 19

19 0.3475 0.4845 0.3333 0.3884 33

20 0.3816 0.4927 1 0.6248 9

21 0.3506 0.3681 0.3672 0.3622 36

22 0.4131 0.4553 0.3672 0.4119 28

23 0.39818 0.4053 0.6649 0.4894 21

24 0.3861 0.4845 0.3911 0.4206 26

25 0.4237 0.4767 1 0.6335 8

26 0.3726 0.4742 0.4299 0.4232 24

27 0.3742 0.4133 0.3911 0.3929 30

28 0.42658 0.4166 0.3333 0.3921 31

29 0.4463 0.4531 0.3672 0.4222 25

30 0.3529 0.3853 0.6649 0.4677 22

31 0.3333 0.451 1 0.5948 12

32 0.3598 0.3333 0.42279 0.3719 35

33 0.3535 0.4622 0.3911 0.3823 34

34 0.3765 0.4872 0.3485 0.4041 29

35 0.3527 0.5104 0.3911 0.4197 27

36 0.416 0.4053 0.3485 0.3899 32

Table 8 Response table for grey relational grade

Factor Level 1 Level 2 Level 3 Min–max

A 0.601517 0.443978 0.157539

B 0.568050 0.533183 0.467008 0.101042

C 0.514683 0.508233 0.545325 0.037092

D 0.516783 0.514058 0.537400 0.023342

E 0.553592 0.498267 0.516383 0.055325

F 0.557917 0.540642 0.469683 0.088233

G 0.516950 0.506683 0.544608 0.037925

H 0.505925 0.534425 0.527892 0.028500

Boldface presentation of data indicates the optimal parameters

Int J Adv Manuf Technol

6 Confirmation tests

The confirmation test for the optimal parameter settingwith its selected levels was conducted to evaluate thequality characteristics for WEDM of Inconel 825.Experiment 4 (Table 7) shows the highest grey relation-al grade, indicating that the optimal process parameterset of A1B1C3D3E1F1G3H2 has the best multiple per-formance characteristics among the 36 experiments,which can be compared with the results of confirmationexperiment for validation of results. Tables 9 and 10show the comparison of the experimental results usingthe orthogonal array (A1B1C1D1E1F2G2H2) and opti-mal grey theory design (A1B1C3D3E1F1G3H2) WEDMparameters on Inconel 825. The response valuesobtained from the confirmation experiment are MRR=126.85 mm3/min, SR=1.44 μm, and SG=0.012 mm.The material removal rate shows an increased value of119.625 to 126.85 mm3/min, the surface roughnessshows a reduced value of 1.68 to 1.44 μm, and thespark gap shows a reduced value of 0.015 to 0.012 mm.The corresponding improvement in material removalrate is 7.22 % and surface roughness and spark gapwere 16.66 and 13.3 %, respectively.

7 Development of mathematical models

The experimental results are used to obtain the mathematicalrelationship between process parameters and machining out-puts. The coefficients of mathematical models are computedusing method of multiple regressions. In this study, Minitab14 (Software Package for Statistical Solutions) was used forthe regression analysis. This software is used to test linearmodels (user defined).

The regression equation is

MRR ¼ −96:7þ 173 Aþ 18:0 Bþ 7:33 C−5:69 D

þ 5:78 E þ 5:73 F þ 9:21 G–5:10 H

S ¼ 33:87 R−Sq ¼ 90:1% R−Sq adjð Þ ¼ 87:2%

The regression equation is

SR ¼ 1:31þ 0:489 Aþ 0:0650 B−0:0104 C−0:0050D−0:0917 E−0:0133 F−0:0921 Gþ 0:0812 H

S ¼ 0:2513 R−Sq ¼ 62:4% R−Sq adjð Þ ¼ 51:3%

Fig. 6 Grey relational grade for maximum MRR, minimum Ra, min-imum spark gap

Main Effects Plot for Means

GEA B C D F H

0.48

0.44

O.52

O.56

0.60

MEAN

1 2 1 2 3 11 1 11 1 2 22 2 2 2 3333 3 3

Fig. 7 The main effects of thefactors on the grey relationalgrade

Fig. 8 Response graph of average grey relational grade

Int J Adv Manuf Technol

The regression equation is

SG ¼ 0:0308−0:00486 Aþ 0:00073 B−0:00323 C þ 0:00031 Dþ 0:00406 E þ 0:00635 F−0:00156 G−0:00135 H

S ¼ 0:01172 R−Sq ¼ 34:4 % R−Sq adjð Þ ¼ 15:0 %

8 Conclusions

In this work, an attempt was made to determine theimportant machining parameters for performance mea-sures like MRR, SF, and SG separately in the WEDMprocess. Factors like pulse on time, pulse off time,corner servo voltage, wire feed rate, wire tension, servofeed, spark gap voltage, and dielectric flow rate havebeen found to play a significant role in rough cuttingoperations for maximizations of MRR, minimization ofsurface roughness, and minimization of spark gap.Taguchi’s experimental design method is used to obtainoptimum parameter combination for maximization ofMRR and minimization of surface roughness as wellas spark gap. Interestingly, the optimal levels of thefactors for all the objectives differ widely. In order tooptimize for all the three objectives, grey relationalanalysis was recommended as a method for optimizing

the complicated interrelationships among multiple per-formance characteristics. As a result, this method greatlysimplifies the optimization of complicated multiple per-formance characteristics, and since it does not involvecomplicated mathematical computations, this can be eas-ily utilized by the stakeholders of the manufacturingworld.

1. The optimal “process parameters” based on grey rela-tional analysis for the wire cut EDM of Inconel 825include 105 μs pulse on time, 50 μs pulse off time, 70 Vcorner servo voltage, 15 kg/cm2 flushing pressure,2 m/min wire feed rate, 9 kg-f wire tension, 30 V sparkgap voltage, and 1,100 mm/min servo feed rate.

2. While applying the grey–Taguchi method, the materialremoval rate shows an increased value of 119.625 to126.85 mm3/min, the surface roughness shows a re-duced value of 1.68 to 1.44 μm, and the spark gapshows a reduced value of 0.015 to 0.013 mm, whichare positive indicators of efficiency in the machiningprocess. Thus, it can be concluded that the grey–Taguchi Method is most ideal and suitable for the para-metric optimization of the wire cut EDM process, whenusing the multiple performance characteristics such asMRR, surface roughness, and spark gap, for machiningthe Inconel 825.

3. Mathematical relations between the machining pa-rameters, namely pulse on time, pulse off time,flushing pressure, corner servo voltage, wire tension,spark gap voltage, servo feed, and wire feed andperformance characteristics such asMRR, SR, and SG areestablished by the regression analysis method. Theestablished mathematical models can be used in estimat-ing the material removal rate, surface roughness, andspark gap without conducting experiments.

Acknowledgments The authors are thankful to the reviewers fortheir suggestions that significantly improved our paper.

Table 10 Optimization results of OA (L36) vs grey theory design

Optimal process parameters

Orthogonal array Grey theory design

Level A1B1C1D1E1F2G2H2 A1B1C3D3E1F1G3H2

MRR (mm3/min) 119.625 126.85

SG (mm) 0.0150 0.013

SR (μm) 1.68 1.44

Table 9 ANOVA for Grey rela-tional Grade Factor Degrees of freedom Sum of squares Mean sum of squares F value % contribution

A 1 0.22337 0.22337 75.552 50.18

B 2 0.0632 0.0316 10.688 14.19

C 2 0.0094 0.0047 1.5852 2.14

D 2 0.0039 0.0020 0.676 0.87

E 2 0.0191 0.0095 2.3132 4.29

F 2 0.0525 0.0262 8.8618 11.79

G 2 0.0092 0.0046 1.5558 2.066

H 2 0.0053 0.0027 0.91324 1.19

Error 20 0.05913 0.0029565

Total 35 0.4451

Int J Adv Manuf Technol

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